Abstract The classic picture of mineral structures is dominated by the periodic repetition of the asymmetric unit over infinite distances. This picture is governed by the principles of symmetry and it has its merits for the description of bulk structures of minerals and their associated equilibrium properties. However, apart from bulk structure, the properties of the actual mineral assemblies found in nature in the form of rocks are equally determined by mineral surfaces, grain boundaries and sub-grain microstructures. These diverse features require a description of minerals at very different length scales, ranging from the properties of atoms at the sub-ångström range (1 Å = 10 −10 m), to the now fashionable nanometre range that would encompass a relatively small and still enumerable number of atoms in a world governed by the forces of quantum mechanics ( Fig. 1 ). Going on to the micrometre length scales of mineral microstructure and further to the length scales directly accessible to the human eye, i.e. millimetre grain sizes or rock deformations ranging from the metre to the kilometre range, the properties of these structures are more and more dictated by classical mechanics. Any consideration of the composition, structure and properties of matter leads to the existence of atoms as its basic building units. Atoms may be approximated as spherical, with a diameter between 1 and 5 × 10 −10 m. However, they are not indivisible (“ατομοσ”) as stated by Democritus, and modern physics of the past 100 years revealed the three fundamental particles protons , electrons , and neutrons .

Abstract Among the structural phase transitions, displacive phase transitions comprise those that only require small collective displacements of individual atoms. A small displacement of atoms in this context amounts to fractions of the nearest neighbour interatomic distances, i.e. generally at most a few tenths of an ångstrom. Displacive transitions occur spontaneously and reversibly at specific pressure and temperature conditions. Because of this, their direct observation is inextricably linked to the use of in situ methods, usually requiring a non-trivial sample environment, e.g. high-pressure cells, furnaces or cryostats. This definition puts displacive phase transitions in contrast to those structural phase transitions that involve significant diffusion of atoms, e.g. cation ordering transitions or entirely reconstructive phase transitions. As this introductory text should serve as a guide to the analysis of experimental data, it will be predominantly concerned with the theory of displacive phase transitions and not with the experimental techniques employed to obtain the necessary data. Alarge number of in-depth review articles and textbooks devoted to the subject has already appeared in the recent past. It is therefore not the aim of this text to introduce every imaginable aspect of displacive phase transitions. Many of the details that are necessarily being omitted can be found elsewhere (e.g. Binder, 1987; Salje, 1992a, 1992c, 1993; Dove, 1997; Carpenter et al., 1998a; Carpenter & Salje, 1998). What this text is trying to achieve is to transport a general picture of the theory and its application to experimental data, accompanied by an explanation of technical terms where they might appear.